A General Approach for Constraint Solving by Local Search

International audienc

Tabu Search for Frequency Assignment in Mobile Radio Networks

International audienc

A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs

A tabu search heuristic for the Equitable Coloring Problem

The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several applications. Due to the hardness of the problem, current exact algorithms can not solve large-sized instances. Such instances must be addressed only via heuristic methods. In this paper we present a tabu search heuristic for the Equitable Coloring Problem. This algorithm is an adaptation of the dynamic TabuCol version of Galinier and Hao. In order to satisfy equity constraints, new local search criteria are given. Computational experiments are carried out in order to find the best combination of parameters involved in the dynamic tenure of the heuristic. Finally, we show the good performance of our heuristic over known benchmark instances

A Recombination-Based Tabu Search Algorithm for the Winner Determination Problem

Abstract. We propose a dedicated tabu search algorithm (TSX_WDP) for the winner determination problem (WDP) in combinatorial auctions. TSX_WDP integrates two complementary neighborhoods designed re-spectively for intensification and diversification. To escape deep local optima, TSX_WDP employs a backbone-based recombination opera-tor to generate new starting points for tabu search and to displace the search into unexplored promising regions. The recombination operator operates on elite solutions previously found which are recorded in an global archive. The performance of our algorithm is assessed on a set of 500 well-known WDP benchmark instances. Comparisons with five state of the art algorithms demonstrate the effectiveness of our approach

Optimality Clue for Graph Coloring Problem

In this paper, we present a new approach which qualifies or not a solution found by a heuristic as a potential optimal solution. Our approach is based on the following observation: for a minimization problem, the number of admissible solutions decreases with the value of the objective function. For the Graph Coloring Problem (GCP), we confirm this observation and present a new way to prove optimality. This proof is based on the counting of the number of different k-colorings and the number of independent sets of a given graph G. Exact solutions counting problems are difficult problems (\#P-complete). However, we show that, using only randomized heuristics, it is possible to define an estimation of the upper bound of the number of k-colorings. This estimate has been calibrated on a large benchmark of graph instances for which the exact number of optimal k-colorings is known. Our approach, called optimality clue, build a sample of k-colorings of a given graph by running many times one randomized heuristic on the same graph instance. We use the evolutionary algorithm HEAD [Moalic et Gondran, 2018], which is one of the most efficient heuristic for GCP. Optimality clue matches with the standard definition of optimality on a wide number of instances of DIMACS and RBCII benchmarks where the optimality is known. Then, we show the clue of optimality for another set of graph instances. Optimality Metaheuristics Near-optimal

Clustering Nominal and Numerical Data: A New Distance Concept for a Hybrid Genetic Algorithm

As intrinsic structures, like the number of clusters, is, for real data, a major issue of the clustering problem, we propose, in this paper, CHyGA (Clustering Hybrid Genetic Algorithm) an hybrid genetic algorithm for clustering. CHyGA treats the clustering problem as an optimization problem and searches for an optimal number of clusters characterized by an optimal distribution of instances into the clusters. CHyGA introduces a new representation of solutions and uses dedicated operators, such as one iteration of K-means as a mutation operator. In order to deal with nominal data, we propose a new definition of the cluster center concept and demonstrate its properties. Experimental results on classical benchmarks are given

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Combining modelled snowpack stability with machine learning to predict avalanche activity

Predicting avalanche activity from meteorological and snow cover simulations is critical in mountainous areas to support operational forecasting. Several numerical and statistical methods have tried to address this issue. However, it remains unclear how combining snow physics, mechanical analysis of snow profiles and observed avalanche data improves avalanche activity prediction. This study combines extensive snow cover and snow stability simulations with observed avalanche occurrences within a random forest approach to predict avalanche situations at a spatial resolution corresponding to elevations and aspects of avalanche paths in a given mountain range. We develop a rigorous leave-one-out evaluation procedure including an independent evaluation set, confusion matrices and receiver operating characteristic curves. In a region of the French Alps (Haute-Maurienne) and over the period 1960–2018, we show the added value within the machine learning model of considering advanced snow cover modelling and mechanical stability indices instead of using only simple meteorological and bulk information. Specifically, using mechanically based stability indices and their time derivatives in addition to simple snow and meteorological variables increases the probability of avalanche situation detection from around 65 % to 76 %. However, due to the scarcity of avalanche events and the possible misclassification of non-avalanche situations in the training dataset, the predicted avalanche situations that are really observed remains low, around 3.3 %. These scores illustrate the difficulty of predicting avalanche occurrence with a high spatio-temporal resolution, even with the current data and modelling tools. Yet, our study opens perspectives to improve modelling tools supporting operational avalanche forecasting.</p

An Analysis of Solution Properties of the Graph Coloring Problem

This paper concerns the analysis of solution properties of the Graph Coloring Problem. For this purpose, we introduce a property based on the notion of representative sets which are sets of vertices that are always colored the same in a set of solutions. Experimental results on well-studied DIMACS graphs show that many of them contain such sets and give interesting information about the diversity of the solutions. We also show how such an analysis may be used to improve a tabu search algorithm